# Phase-space continuity equations for quantum decoherence, purity, von Neumann and R\'enyi entropies

## TL;DR

This paper derives phase-space continuity equations for quantum information measures like purity, von Neumann, and Rényi entropies, providing insights into quantum decoherence and non-classicality in anharmonic systems.

## Contribution

It introduces a set of phase-space continuity equations for quantum information measures, extending the analysis to Rényi entropy and enhancing understanding of quantum decoherence.

## Key findings

- Non-classicality profiles can be characterized by fluxes of probability, purity, and von Neumann entropy.
- Phase-space quantifiers are extended to include Rényi entropy.
- The approach offers a unified framework for analyzing quantum decoherence in anharmonic systems.

## Abstract

Phase-space features of the Wigner flow are examined so to provide a set of continuity equations that describe the flux of quantum information in the phase-space. The reported results suggest that the non-classicality profile of anharmonic (periodic) quantum systems can be consistently obtained in terms of the fluxes of probability, purity and von Neumann entropy. Extensions of the such phase-space quantifiers are also investigated in the context of the so-called R\'enyi entropy.